We propose two efficient automatic differentiation (AD) schemes to compute incrementally Taylor series and System Jacobian for solving differential-algebraic equations (DAEs) by Taylor series. Our schemes are based on topological ordering of a DAE’s computational graph and then partitioning the topologically sorted nodes using structural information obtained from the DAE. Solving a DAE by Taylo...

The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for ”learning” piecewise linear scalar functions in two settings we term ”approximation” (where an ”oracle” outputs accurate functi...

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in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...